MOS Transistor Theory (Deep Submicron Effects) Chapter 2 MOS Transistor Theory (Deep Submicron Effects)

Simplified Transistor Model From TSMC035 N-transistor model User defined VGS = 3V VDS=3V ID= 574 mA VGS = 3V VDS=1V ID= 373 mA VGS = 2V VDS=1V ID= 182 mA VGS = 2V VDS=3V ID= 201 mA Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Lab 2: Transistor Design W= 6l = 1,2mm L=6l = 1,2mm Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Lab 2: Simulated Curves VGS = 2V VDS=1V ID= 95 mA VGS = 2V Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Comparing Model Results Vgs (V) ID (mA) (Vds=1V) ID (mA) (Vds=3V) simulated simplified Error (%) 2V 95 182 92 100 201 101 3V 178 373 109 231 574 111 Being the simulated results quite accurate, the simplified model produces very over-estimated values !! Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Velocity Saturation VDS produces an electric field from Drain to Source In old large transistor technology (large L): Fields are low (remember, for electric field E, potential difference DV and distance d: E=DV/d) Carrier drift velocity is proportional to E. In Deep Submicron Technologies (small L): d is very small, and longitudinal electric field is high Field gets to a critical value, Ecrit, reducing mobility. Carrier drift velocity is not proportional to E anymore; velocity saturates. Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Velocity Saturation (contn´d) Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Traditional vsat model Well before pinch-off (VDS = VGS-VTH), ID reaches to a saturation value due to velocity saturation (vsat is a SPICE technological parameter). Simplifying assumptions are adopted: Velocity saturates abruptly at Ecrit ; vsat= mn.Ecrit VDSAT due to velocity saturation is constant (for any VGS); VDSAT = L.Ecrit = L. vsat /mn If VGS-VTH < VDSAT, saturation occurs by pinch-off (we use the simplified ID saturation equation) If VGS-VTH > VDSAT, saturation occurs by velocity saturation  IDSAT = kn. [(VGS-VTH). VDSAT-VDSAT2 /2] Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Applying vsat model vsat = 1,58 X 105 m/s VDSAT = L. vsat /mn = 1,2x10-6. 1,58 X 105 /421,39X10-4 = 4,49V Observe that for L=1,2mm, since VDSAT is very high, pinch-off (VGS-VTH) will occur first !! But, for L=0,4mm, VDSAT = 1,5 V Therefore, for VGS= 3V, VGS-VTH=2,45V, and pinch-off will not occur since saturation occurs first, for VDS = =VDSAT = 1,5 V Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Applying vsat model (contn´d) Simulation was performed again for W=L=0,4mm In vsat model, vsat = 1,58 X 105 m/s; VDSAT = 1,5 V Vgs (V) ID (mA) (Vds=1V) ID (mA) (Vds=3V) simulated simplified vsat 2V 75 (95) 182 ?? 81 (100) 201 3V 146 (178) 373 159 (231) 574 W=L=1,2mm Observations: Simplified model values are the same as before. Why? For 0,4 mm, LEVEL 53 model shows its effectiveness Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Computing ID by vsat model VDSAT= 1,5V A) VGS-VTH < VDSAT (pinch-off) IDSAT = kn. (VGS-VTH) 2./2 B) VGS-VTH > VDSAT (velocity saturation) IDSAT = kn. [(VGS-VTH). VDSAT-VDSAT2 /2] ( the current is linear to VGS) VGS=2V  VGS-VTH= 1,45V  Case A or B? VGS=3V  VGS-VTH= 2,45V  Case A or B?

Applying vsat model-2 Simulation was performed again for W=L=0,4mm In vsat model, vsat = 1,58 X 105 m/s; VDSAT = 1,5 V Vgs (V) ID (mA) (Vds=1V) ID (mA) (Vds=3V) simulated simplified w/ vsat 2V 75 182 81 201 3V 146 373 159 574 488 Observation: vsat model still over-estimates values of ID Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 2-12

Mobility Degradation Up to now, VDSAT is the same for any VGS Transversal electrical field due to VGS is also critical for Deep Submicron Technologies (vertical dimensions are also small) Relatively high values of transversal electrical field leads to carrier scattering and mobility degradation The values of mn and mp are smaller than the ideal ones These effects are taken into account in the SPICE model LEVEL 53 Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

Empirical a-law model a-law is a simplified empirical model including: Mobility degradation Velocity saturation It is not part of SPICE models ID is given as: 0 (VGS<VTH : cutoff) IDSAT.VDS/VDSAT (VDS<VDSAT : linear) IDSAT (VDS>VDSAT : saturation) IDSAT= Pc.(b/2) .(VGS-VTH)a ; VDSAT= Pv.(VGS-VTH) a/2 Pc, Pv and a are empirically extracted parameters Copyright © 2005 Pearson Addison-Wesley. All rights reserved.

a-law model example Observations: 1. Shockley is the simplified model 2. Values of Pc, Pv and a are not provided in this example Copyright © 2005 Pearson Addison-Wesley. All rights reserved.